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Restoring Depth to Leonardo’s Mona Lisa

Smiling serenely behind bullet-proof glass, the painting titled La Gioconda, or the Mona Lisa, receives about 6 million visitors per year at its alcove at the Louvre Museum in Paris. More popular than ever at 500 years of age, the portrait depicts a young woman of uncertain identity-most likely the wife of a wealthy silk merchant-seated before a somewhat idealized Italian landscape. Despite its singular fame, the Mona Lisa is not one of a kind. In fact, another Gioconda graces the permanent collection of the Prado Museum in Madrid.

Although it strongly resembles the Mona Lisa, the portrait in Madrid had long been considered an insignificant copy of Leonardo da Vinci’s masterpiece, mainly on account of its dull black background. From time to time, art historians and critics had offered various theories about a connection between the two paintings, but it was only in 2010 that curators at the Louvre itself requested a close analysis of the “other” Gioconda portrait. In the words of the official report from the Prado, “The extremely interesting results obtained from the comparison of the infrared reflectograph of the Prado’s panel with the one of the original painting led to the decision to undertake a more detailed study of the Prado’s painting and subsequently to restore it.” Because we had already conducted some psychological research of our own on Leonardo’s masterpiece, focusing on La Gioconda’s absorbing smile, we were naturally interested in the Prado’s work in restoring this sister painting.

The first stage of the analysis immediately brought surprising results: the black background had not been part of the initial composition. Because infrared reflectography revealed the layer of black paint to contain linseed oil, which did not come into use on canvas until after 1750, experts knew it could only have been added centuries after Leonardo completed his work. As for why it was added, the report from the Prado characterizes the original background landscape as “not entirely finished,” speculating that it may have been painted over for that reason. The Prado analysts also detected “an organic layer that was probably a varnish” in between the landscape background and the dull black overpainting.

After two years of technical scrutiny by means of x-ray, ultraviolet-induced visible fluorescence, a binocular magnifier, and multiple chemical tests, followed by careful restoration, the Gioconda returned to the Prado for public viewing. The long process of examination brought a wealth of new knowledge about this painting: Not only had removal of the black overpainting uncovered a detailed landscape background closely resembling that of the Mona Lisa, but the experts had identified (again, by infrared reflectography) several corrections that appeared in both the Louvre and the Prado versions. Some of these corrections, such as adjustments made in the position of the fingers, were visible even in the bottommost layers.

The implications are striking. Almost certainly, the individual who painted the Prado Gioconda was witness to the entire process of creation of one of the most famous paintings in the world. By this reasoning, the Prado Gioconda is itself a product of Leonardo da Vinci’s studio, produced simultaneously with the Mona Lisa. For all the two portraits have in common, a side-by-side comparison makes it clear that they differ in two major ways: perspective and coloring. The difference in perspective is apparent, for example, in the right armrest of the sitter’s chair, which can be seen in the Prado version but not in the Louvre version. The sitter’s hands, as well, display a shift in perspective between the two paintings.

To understand the significance of this perspectival shift, we started by trying to get an exact measure of it. We calculated the difference between the two images by comparing pairs of unequivocal landmarks found in both paintings, such as the angle formed at the point where the upper and lower eyelids meet, the labial angle (the degree to which the nose is rotated up or down relative to the facial plane), and the tip of the nose. We found, however, in the area of the face, any differences we could measure were minimal; in fact, a bidimensional regression on the pairs of landmarks revealed a correlation of 99.8 percent. It was in the lower portion of each portrait, particularly in the area around the hands, that a systematic horizontal divergence between the two versions became apparent.

On the basis of the perspectival difference between the two versions of the Gioconda, we can try to reconstruct the studio setting the painters chose for working on the portraits. To that end, we asked 32 participants in a psychological experiment to inspect the Louvre and the Prado versions side by side and to estimate the angle and distance between the likely positions of the two painters.

The first finding of this study, and the most significant, was that even people who are not specially trained could detect with the naked eye the difference in perspective between the two paintings. Second, on the whole, the estimates suggested the painter of the Prado version was standing not only to the left but also closer to the sitter than Leonardo. The angle between the two painters’ perspectives was apparently very small: An average of the participants’ estimates yielded a disparity between the two portraits of 69.3 millimeters. This measurement, which perhaps does not sound significant in itself, is actually very close to what several international anthropometric studies have found to be the average distance between the pupils of the two eyes of adult Italian males, 64.1 millimeters-a point worth noting in the context of binocular vision and depth perception. So far, we have two brilliantly executed oil paintings that correspond to each other in many fine details but differ in one essential point: the perspective. Moreover, the difference in perspective closely approximates that found between the two eyes of the adult male face. This opens up a unique opportunity: We can now compile a 3D image of the Mona Lisa.

The lower part of the portraits seems interesting in this regard, as the divergence between the Louvre and the Prado versions there best fits the systematic horizontal divergence necessary to create a 3D image. The impression of depth is most striking in the area of the Mona Lisa’s hands, which apparently lie in front of her figure and closer to the viewer. In the area around the face this 3D effect appears as well, although here it is less vivid because the pattern of divergence is not strictly horizontal.

The difference between the upper and lower parts of the painting could indicate several things: that the perspective of the painter(s) changed in the course of the creative process, for instance, or that the two artists worked out some parts of their paintings in parallel whereas for other parts one painter simply copied the other’s version; at this point we do not know. In any case, it’s important to note that the perception of depth produced by compiling the two portraits is not merely an impression or an optical illusion but has a solid basis in mathematics. We can test this in the area of the hands, for example, by submitting the stereogram to an algorithm developed by Wim Abbeloos, of the University of Leuven, for back-calculating 3D information, called the Fast MatlabStereo Matching Algorithm.

We know from Leonardo’s artistic but not entirely systematic notebooks that he was pondering the problem of how to depict 3D information on a two-dimensional canvas: On the facing page, at top, a sketch he made in preparation for his altarpiece painting Adoration of the Magi shows the meticulous care with which he planned a complex scene. From his notebooks, we also know (as shown on the facing page, at bottom) that he pondered at length the workings of binocular vision, developing a theory to account for the differential occlusion of objects as seen from the different perspectives of the two eyes. In fact, Leonardo was one of the few painters-of the Renaissance or of any period since then-to study 3D vision so intensively.

There is no proof in the notebooks, however, that he came to the correct answer in the end, identifying binocular disparity as the basis of stereovision or stereopsis. Today, influential vision scientists such as Nicholas Wade, Emeritus Professor in the Department of Psychology at the University of Dundee, Scotland, therefore assume Leonardo never took that essential final step.

Nevertheless, more than three centuries before the stereoscope (the first standard device capable of displaying 3D images) was invented by British scientist Charles Wheatstone, Leonardo created a pair of oil paintings in which certain areas, although not the entire work, meet the criteria for producing a 3D image.

The Eye of the Beholder

In spite of all their points of resemblance, the Louvre’s Mona Lisa, with the somber color spectrum it bears today, at first glance appears very different from the brighter portrait in the Prado. In reality, the apparent difference is mainly superficial and is due to the effect of selective aging on the different varnishes applied to the surface of the Louvre portrait, as well as to the full restoration of the Prado version only recently.

Leonardo applied color in many fine layers, in a technique called sfumato, which allowed him to avoid harsh, contrasts between areas of light and shade in his painting; indeed, he is known for the subtlety of these transitions. For the restorer, however, these numerous thin layers of paint-some of which may include varnish mixed in with the pigment-pose a problem, because they make it very difficult to remove the varnish without damaging the painting. Fortunately, techniques of computer imaging available today make it possible to cancel out the dark-yellowing effect without actually touching the canvas.

The varnish on the Mona Lisa has undeniably altered the painting’s original appearance, but does it detract from its beauty? As psychologists, we saw in the two portraits-the world famous, yellowed Mona Lisa from the Louvre and the lesser-known, bluer and altogether more colorful Gioconda from the Prado-the basis for an interesting experiment. The present day Mona Lisa, with its yellow-brown tint, is generally acknowledged as a masterpiece, but would it keep this status when considered in comparison with the Prado’s Gioconda with its fresher, brighter palette? We wanted to find out whether the Mona Lisa might owe some of her aesthetic appeal purely to familiarity.

Our research participants were 63 college-aged women and men who had no particular training in the arts (and no knowledge as to the purpose of our experiment). Dividing them into two roughly equal groups, we required one group to study the Louvre portrait closely for 10 minutes in order to answer a set of very specific questions about its color composition, features of the landscape in the background, and even the state of mind they inferred from the model’s expression. The other group carried out the same procedure with the Prado portrait. We then used techniques of computer morphing and warping to produce images that were intermediate between the portrait in the Louvre and that in the Prado, and asked the participants to rate each version of the portrait according to its artistic quality and to their personal liking for it.

For the first group-participants who had spent some time looking closely at the Louvre portrait-the more “Louvresque” a specific image was, the more highly participants rated its artistic quality and the more they liked it. By contrast, the group of subjects who had had the opportunity to study the Prado version extensively in the first stage of our experiment showed no clear personal preference for either the Prado-like or the Louvrelike versions; however, they rated the Prado-like versions more highly in terms of artistic quality.

Our findings suggest the commonly observable preference for the Louvre version might actually be based on familiarity rather than quality alone, and that cognitive processes yielding acquaintance can well cause a preferential shift, for instance, towards the Prado version.

Looking into the Background

In addition to what they tell us about Leonardo’s work on the challenge of depicting 3D subjects on a two-dimensional canvas, the pair of Gioconda portraits shed some light on a lingering question in art history: Does the background of the Gioconda paintings depict an actual landscape glimpsed through an open window or another canvas painted to provide the effect of a landscape in the background? This admittedly minor point has vexed art historians for some time, because no direct evidence is known to exist for the model of this background, including the location and nature of the loggia positioned between the sitter and the landscape.

As long as only one depiction of the landscape was available, the question had to remain open. Taking the pair of Giocondas as two renderings of the same scene, however, allows us to apply mathematical reasoning to any differences we can measure in the positions of the landmarks between the two. We can analyze the different trajectories that emerge between the paintings in, say, the tip of a mountain, the idiosyncratic ragged edges of rocks, or the plinth of a column. The results, apart from some slight deviations detected in the upper part of the mountainside, show a nearly perfect constant expansion pattern of 10 percent from the Louvre painting to that in the Prado. Very near objects such as the items of the loggia show the same expansion factor as the icy mountains situated at the farthest distance of the composition.

Clearly, this pattern is not compatible with the way objects would appear in an actual landscape. The logical conclusion is that Leonardo’s model was sitting not in a loggia but in the artist’s studio in front of a flat decorated canvas.

Such insights are often owed to the approach and methodology of natural sciences, which underlines the importance of integrating their enriching potential into arts and aesthetics research. A newly emerging joint science of aesthetics can provide a fascinating and powerful framework for future research on aesthetics. As an example, we are currently collaborating with researchers at the Smith-Kettlewell Eye Research Institute, in San Francisco, to test the surprising hypothesis that the Dutch artist Vermeer developed and secretly applied optic devices for creating his stunning, photographically appealing paintings. In another project, together with artists at the Cardiff School of Art in Wales, we are investigating how the geometry of a painting would best simulate the viewer’s everyday habits of perception. With studies of this kind, the science of aesthetics offers an opportunity for reconsidering unsolved questions and opens new perspectives on not-yet-questioned issues in a thrilling interdisciplinary way.